Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,34,37,30)(27,31)(28,33)(29,32)(35,52,53,44)(36,50,41,45)(38,55,54,46)(39,48)(40,47)(42,51)(43,49);(24,26)(25,30)(27,38)(28,41)(29,37)(31,46)(32,34)(33,50)(35,39)(36,43)(40,54)(42,53)(44,48)(45,49)(47,55)(51,52);(21,23)(24,27,29,40)(25,31,32,47)(26,35,37,53)(28,42,43,39)(30,44,34,52)(33,51,49,48)(36,54,41,38)(45,55,50,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4001);